A study on inventory modeling through matrices. (English) Zbl 1317.90037
Summary: An intention of this paper is to study the inventory modelling through matrices and establish the optimum results such as economic order quantity and total inventory cost by using matrix operations. We define various factors which are affecting the inventory cost by using the diagonal matrices. We developed the computation algorithm to test the effectiveness of the model through numerical example.
MSC:
| 90B05 | Inventory, storage, reservoirs |
| 15A15 | Determinants, permanents, traces, other special matrix functions |
| 90-02 | Research exposition (monographs, survey articles) pertaining to operations research and mathematical programming |
Keywords:
inventory; matrix; diagonal matrix; trace of matrix; ordering diagonal matrix; total cost diagonal matrixReferences:
| [1] | Churchman, C.W., Ackoff, R.L., Arnoff, F.L.: Introduction to Operations Research. Wiley, New York (1957) · Zbl 0079.35905 |
| [2] | Hadley, G., Whitin, T.M.: Analysis of Inventory Systems. Prentice Hall, Englewood Cliffs (1963) · Zbl 0133.42901 |
| [3] | Eriksen, E.: Principal Minors and the Hessian, Lecturer Notes 5. BI Norwegian management, Department of Economics, Norway (2010) |
| [4] | Levin, R.I., McLaughlin, C.P., Lamone, R.P., Kottas, J.F.: Productions/Operations Management: Contemporary Policy for Managing Operating Systems. McGraw-Hill, New York (1972) |
| [5] | Silver, E.A., Peterson, R.: Decision, Systems for Inventory Management and Production Planning, 2nd edn. Wiley, New York (1985) |
| [6] | Banerjee, A.: A joint economic lot-size model for purchaser and vendor. Decis. Sci. 17, 292-311 (1986) · doi:10.1111/j.1540-5915.1986.tb00228.x |
| [7] | Goyal, S.K.: A joint economic-lot-size model for purchaser and vendor: a comment. Decis. Sci. 19, 236-241 (1988) · doi:10.1111/j.1540-5915.1988.tb00264.x |
| [8] | Baker, R.C., Urban, T.L.: A deterministic inventory system with an inventory level dependent demand rate. J. Oper. Res. Soc. 39, 823-831 (1988) · Zbl 0659.90040 · doi:10.1057/jors.1988.142 |
| [9] | Padmanabhan, G., Vrat, P.: Analysis of multi-item inventory systems under resource constraints: a non-linear goal programming approach. Eng. Costs Prod. Econ. 20, 121-127 (1990) · doi:10.1016/0167-188X(90)90096-Z |
| [10] | Datta, T.K., Pal, A.K.: A note on an inventory model with inventory level dependent demand rate. J. Oper. Res. Soc. 41, 971-975 (1990) · Zbl 0725.90028 · doi:10.1057/jors.1990.149 |
| [11] | Urban, T.L.: An inventory model with an inventory-level-dependent demand rate and relaxed terminal conditions. J. Oper. Res. Soc. 43, 721-724 (1992) · Zbl 0825.90335 · doi:10.1057/jors.1992.103 |
| [12] | Pal, S., Goswami, A., Chaudhuri, K.S.: A deterministic inventory model for deteriorating items with stock-dependent rate. Int. J. Prod. Econ. 32, 291-299 (1993) · doi:10.1016/0925-5273(93)90043-K |
| [13] | Bar-Lev, S.K., Parlar, M., Perry, D.: On the EOQ model with inventory-level-dependent demand rate and random yield. Oper. Res. Lett. 16, 167-176 (1994) · Zbl 0816.90052 · doi:10.1016/0167-6377(94)90028-0 |
| [14] | Gerchak, Y., Wang, Y.: Periodic-review inventory models with inventory-level dependent demand. Nav. Res. Logist. 41, 99-116 (1994) · Zbl 0799.90045 · doi:10.1002/1520-6750(199402)41:1<99::AID-NAV3220410107>3.0.CO;2-W |
| [15] | Padmanabhan, G., Vrat, P.: EOQ models for perishable items under stock dependent selling rate. Eur. J. Oper. Res. 86, 281-292 (1995) · Zbl 0906.90054 · doi:10.1016/0377-2217(94)00103-J |
| [16] | Ray, J., Chaudhuri, K.S.: An EOQ model with stock-dependent demand, shortage, inflation and time discounting. Int. J. Prod. Econ. 53, 171-180 (1997) · doi:10.1016/S0925-5273(97)00112-6 |
| [17] | Roy, T.K., Maiti, M.: Multi-objective inventory models of deteriorating items with some constraints in a fuzzy environment. Comput. Oper. Res. 25, 1085-1095 (1998) · Zbl 1042.90511 · doi:10.1016/S0305-0548(98)00029-X |
| [18] | Hwang, H., Hahn, K.H.: An optimal procurement policy for items with an inventory level-dependent demand rate and fixed lifetime. Eur. J. Oper. Res. 127, 537-545 (2000) · Zbl 0982.90003 · doi:10.1016/S0377-2217(99)00337-9 |
| [19] | Datta, T.K., Paul, K.: An inventory system with stock-dependent, price-sensitive demand rate. Prod. Plan. Control 12, 13-20 (2001) · doi:10.1080/09537280150203933 |
| [20] | Kar, S., Bhunia, A.K., Maiti, M.: Inventory of multi-deteriorating items sold from two shops under single management with constraints on space and investment. Comput. Oper. Res. 28, 1203-1221 (2001) · Zbl 0980.90007 · doi:10.1016/S0305-0548(00)00034-4 |
| [21] | Sana, S.S.: Price-sensitive demand for perishable items—an EOQ model. Appl. Math. Comput. 13(217), 6248-6259 (2011) · Zbl 1208.90011 · doi:10.1016/j.amc.2010.12.113 |
| [22] | Sana, S.S.: An EOQ model for salesmen’s initiatives, stock and price sensitive demand of similar products-A dynamical system, Appl. Math. Comput. 7(218), 3277-3288 (2011) · Zbl 1239.90007 |
| [23] | Cárdenas-Barr��n, L.E., Treviño-Garza, G., Wee, H.M.: A simple and better algorithm to solve the vendor managed inventory control system of multi-product multi-constraint economic order quantity model. Expert Syst. Appl. 39, 3888-3895 (2012) · doi:10.1016/j.eswa.2011.09.057 |
| [24] | Sana, S.S.: The EOQ model—a dynamical system. Appl. Math. Comput. 17(218), 8736-8749 (2012) · Zbl 1245.90006 · doi:10.1016/j.amc.2012.02.032 |
| [25] | Sana, S.S.: An economic order quantity model for nonconforming quality products. Serv. Sci. 4(4), 331-348 (2012) · doi:10.1287/serv.1120.0027 |
| [26] | Sana, S.S.: An EOQ model for stochastic demand for limited capacity of own warehouse. Ann. Oper. Res., 1-17 (2013). doi:10.1007/s10479-013-1510-5 |
| [27] | Cárdenas-Barrón, L.E., Sarkar, B., Treviño-Garza, G.: An improved solution to the replenishment policy for the EMQ model with rework and multiple shipments. Appl. Math. Model. 37, 5549-5554 (2013) · Zbl 1426.90012 · doi:10.1016/j.apm.2012.10.017 |
| [28] | De, S.K., Sana, S.S.: Backlogging EOQ model for promotional effort and selling price sensitive demand—an intuitionistic fuzzy approach. Ann. Oper. Res. 1-20 (2013). doi:10.1007/s10479-013-1476-3 · Zbl 1325.90007 |
| [29] | Tayal, S., Singh, S.R., Sharma, R., Chauhan, A.: Two echelon supply chain model for deteriorating items with effective investment in preservation technology. Int. J. Math. Oper. Res. 6, 84-105 (2014) · Zbl 1390.90044 · doi:10.1504/IJMOR.2014.057854 |
| [30] | De, S.K., Goswami, A., Sana, S.S.: An interpolating by pass to Pareto optimality in intuitionistic fuzzy technique for a EOQ model with time sensitive backlogging. Appl. Math. Comput. 230, 664-674 (2014) · Zbl 1410.90010 · doi:10.1016/j.amc.2013.12.137 |
| [31] | Tsoularis, A.: Deterministic and stochastic optimal inventory control with logistic stock-dependent demand rate. Int. J. Math. Oper. Res. 6, 41-69 (2014) · Zbl 1390.90047 · doi:10.1504/IJMOR.2014.057851 |
| [32] | Pal, B., Sana, S.S., Chaudhuri, K.: Joint pricing and ordering policy for two echelon imperfect production inventory model with two cycles. Int. J. Prod. Econ. 155, 229-238 (2014) · doi:10.1016/j.ijpe.2013.11.027 |
| [33] | Cárdenas-Barrón, L.E., Treviño-Garza, G., Widyadana, G.A., Wee, H.-M.: A constrained multi-products EPQ inventory model with discrete delivery order and lot size. Appl. Math. Comput. 230, 359-370 (2014) · Zbl 1410.90004 · doi:10.1016/j.amc.2013.12.077 |
| [34] | Soni, H.N., Patel, K.A.: Optimal policies for vendor-buyer inventory system involving defective items with variable lead time and service level constraint. Int. J. Math. Oper. Res. 6, 316-343 (2014) · Zbl 1390.90042 · doi:10.1504/IJMOR.2014.060851 |
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